Algebra Examples

$\frac{11 π}{12} = \frac{3 π}{4} + \frac{π}{6}$

Step 1

Move all terms not containing a variable to the right side of the equation.

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Step 1.1

Subtract $\frac{11 π}{12}$ from both sides of the equation.

$0 = \frac{3 π}{4} + \frac{π}{6} - \frac{11 π}{12}$

Step 1.2

Find the common denominator.

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Step 1.2.1

Multiply $\frac{3 π}{4}$ by $\frac{3}{3}$ .

$0 = \frac{3 π}{4} \cdot \frac{3}{3} + \frac{π}{6} - \frac{11 π}{12}$

Step 1.2.2

Multiply $\frac{3 π}{4}$ by $\frac{3}{3}$ .

$0 = \frac{3 π \cdot 3}{4 \cdot 3} + \frac{π}{6} - \frac{11 π}{12}$

Step 1.2.3

Multiply $\frac{π}{6}$ by $\frac{2}{2}$ .

$0 = \frac{3 π \cdot 3}{4 \cdot 3} + \frac{π}{6} \cdot \frac{2}{2} - \frac{11 π}{12}$

Step 1.2.4

Multiply $\frac{π}{6}$ by $\frac{2}{2}$ .

$0 = \frac{3 π \cdot 3}{4 \cdot 3} + \frac{π \cdot 2}{6 \cdot 2} - \frac{11 π}{12}$

Step 1.2.5

Reorder the factors of $4 \cdot 3$ .

$0 = \frac{3 π \cdot 3}{3 \cdot 4} + \frac{π \cdot 2}{6 \cdot 2} - \frac{11 π}{12}$

Step 1.2.6

Multiply $3$ by $4$ .

$0 = \frac{3 π \cdot 3}{12} + \frac{π \cdot 2}{6 \cdot 2} - \frac{11 π}{12}$

Step 1.2.7

Reorder the factors of $6 \cdot 2$ .

$0 = \frac{3 π \cdot 3}{12} + \frac{π \cdot 2}{2 \cdot 6} - \frac{11 π}{12}$

Step 1.2.8

Multiply $2$ by $6$ .

$0 = \frac{3 π \cdot 3}{12} + \frac{π \cdot 2}{12} - \frac{11 π}{12}$

Step 1.3

Combine the numerators over the common denominator.

$0 = \frac{3 π \cdot 3 + π \cdot 2 - 11 π}{12}$

Step 1.4

Simplify each term.

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Step 1.4.1

Multiply $3$ by $3$ .

$0 = \frac{9 π + π \cdot 2 - 11 π}{12}$

Step 1.4.2

Move $2$ to the left of $π$ .

$0 = \frac{9 π + 2 π - 11 π}{12}$

Step 1.5

Add $9 π$ and $2 π$ .

$0 = \frac{11 π - 11 π}{12}$

Step 1.6

Subtract $11 π$ from $11 π$ .

$0 = \frac{0}{12}$

Step 1.7

Divide $0$ by $12$ .

$0 = 0$

Step 2

Since $0 = 0$ , the equation will always be true.

Always true